Answer:
I am the home for feathery animals.
I have a name that's not mine and no one cares about me in their prime. People cry at my sight and lie by me all day and night.
I'm not a bird, but I can fly through the sky. I'm not a river, but I'm full of water. What am I?
I am a daily ritual involving using a metal tool on the body
When you take away the whole from me, there is always some left. What am I?
No matter how little or how much you use me, you change me every month.